An example of a harmonic map between Euclidean balls
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- by Antonios D. Melas PDF
- Proc. Amer. Math. Soc. 117 (1993), 857-859 Request permission
Abstract:
Here we construct a homeomorphism of the unit sphere in three-dimensional Euclidean space to itself whose harmonic extension in the unit ball is not a diffeomorphism.References
- Gustave Choquet, Sur un type de transformation analytique généralisant la représentation conforme et définie au moyen de fonctions harmoniques, Bull. Sci. Math. (2) 69 (1945), 156–165 (French). MR 16973 H. Kneser, Lösung der Aubgabe $41$, Jber. Deutsch. Math.-Verein. 35 (1926), 123-124. T. Radó, Augabe $41$, Jber. Deutsch. Math.-Verein. 35 (1926), 49.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 857-859
- MSC: Primary 58E20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1112497-9
- MathSciNet review: 1112497